The sum of the first 10 terms of the geometric progression that is given in the question is 1023.
What is geometric progression ?
Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.
The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.
The sum of the first n terms of a geometric progression is given by the formula:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Using this formula, we can find the sum of the first 10 terms of the given series as:
[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]
[tex]= 1(1 - 1024) / (-1)[/tex]
[tex]= 1023[/tex]
Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.
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an item on sale costs 60 of the original price. if the original price was $80 what is the sale price 82 whats the sales price
The sales price of the item is $48.
The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32
$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.
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WILL MARK BRAINLIEST draw the right triangle (show your process)
Answer:[tex]3\sqrt{2}[/tex]
Step-by-step explanation:
in order to make a right triangle point should be either (1,4) or (4,1)
each way hypotenuse of this triangle is
[tex]known coordinates are (4,4)-- > (x1,y1)\\ and (1,1)-- > (x2,y2) \\\sqrt{(x1-x2)^{2}+(y1-y2)^{2}} =\sqrt{(4-1)^{2}+(4-1)^{2}}=\sqrt{9+9}=\sqrt{3^{2}*2}=3\sqrt{2}[/tex]
i-Ready
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Which division expression is shown in the model?
1
col
3
÷2
314
÷2 2÷
Divide Fractions: Fractional Quotients Quiz - Level F
13
2
3
-
+ +
3
The division expression shown in the model attached to this question is 1/2 ÷ 3
How to determine which division expression is shown in the model?The model missing in the question is added as an attachment
In the model, we have
Shaded sections = 3
Partitons = 1/2
This means that
Division expression = Partitons ÷ Shaded sections
Substituting the above expressions, we have
Division expression = 1/2 ÷ 3
This means that the division expression is 1/2 ÷ 3
When the expression is solved, we have
Division expression = 1/6
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Complete question
Which division expression is shown in the model?
See attachment
2x^4 −15x^3 +27x^2 +2x +8 is divided by x−4
Answer:
Step-by-step explanation:
Standard: 2x^3 - 7x^2 -x-2
Quotient: 2x^3- 7x^2 -x-2
remainder: 0
The difference between
two numbers is 3. Their
sum is 47. What are the
numbers?
Answer:
25 and 22
Step-by-step explanation:
A house on the market was valued at $442,000. After several years, the value decreased by 15%. By how much did the house's value decrease in dollars? What is the current
Let X be the time that Alice waits for a traffic light to turn green, and let Y be the time (at a different intersection) that Bob waits for a traffic light to turn green. Suppose that X and Y have joint density
f(x,y)=15e−3x−5y,x≥0,y≥0
The variance of 2X+3Y is
The variance of 2X + 3Y is 35.52.
The solution to the problem is as follows:
First, find the mean and variance of X and Y:
E(X) = 3/5
Var(X) = 3/25
E(Y) = 1
Var(Y) = 1/25
Then, use the properties of variance to find the variance of 2X + 3Y:
Var(2X + 3Y)
= 4Var(X) + 9Var(Y) + 12Cov(X,Y)Cov(X,Y)
= E[(2X - 6/5)(3Y - 1)]
= 6E(XY) - 6E(X) - 3E(Y) + 2
= 6 * (integral from 0 to infinity integral from 0 to infinity of xyf(x,y)dxdy) - 6 * 3/5 - 3 * 1 + 2 = 6 * (integral from 0 to infinity 15xye^-3xdydx) - 8
= 54/5
Therefore,
Var(2X + 3Y) = 4(3/25) + 9(1/25) + 12(54/5)
= 888/25
= 35.52.
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What is the answer to
(P-q) (3)
Answer:
3P-3q
Step-by-step explanation:
you want to distribute the 3, to the whole parenthesis.
Can anyone help me with this? i have 6 problems like this and I don't know how to solve them.
1. y=x+4
y = 3x
2. x=-2y+1
x-y=-5
3. y=x-7
2x+y=8
4. y=3x-6
-3x+y=-6
5. x+2y=200
x=y+50
6. 4x+3y=1
x=1-y
Its Solving Using Substitution. It's also due tomorrow so please help.
Answer:
Sure, I can help you solve these problems using substitution. Let's start with problem 1:1. y=x+4 y=3x To solve this system of equations, we need to substitute one of the variables from one equation into the other equation. We can solve the second equation for y:y=3x Now we can substitute this expression for y into the first equation:y=x+4 3x=x+42x=4x=2 Now we can substitute this value for x into either equation to solve for y:y=x+4 y=2+4y=6 So the solution to this system of equations is x=2, y=6. You can follow the same procedure to solve the rest of the problems. 2. x=-2y+1 x-y=-53. y=x-7 2x+y=84. y=3x-6 -3x+y=-65. x+2y=200 x=y+506. 4x+3y=1 x=1-y Let me know if you need any further assistance.
let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. which of the following is a possible graph of y=f(x)?
First, note that the degree of the polynomial is the highest power of x that appears in the expression. In this case, the degree is max(n, 5, m, 2).
How to determine graph?Next, consider the leading coefficient of the polynomial, which is the coefficient of the term with the highest power of x. In this case, the leading coefficient is a.
Based on this information, here are some possible general shapes of the graph of y=f(x):
If n is even and a > 0, the graph of y=f(x) looks like a "U" shape, with both ends pointing upwards.
If n is even and a < 0, the graph of y=f(x) looks like an upside-down "U", with both ends pointing downwards.
If n is odd and a > 0, the graph of y=f(x) looks like a "v" shape, with the vertex pointing upwards.
If n is odd and a < 0, the graph of y=f(x) looks like an upside-down "v", with the vertex pointing downwards.
Note that these are just general shapes, and the actual graph could be modified by the other terms in the polynomial. Additionally, the values of b, c, d, and the constants could also affect the shape and behavior of the graph.
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Complete Question is : let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. what is the possible graph of the function?
Ming took a cab across town. His fare was $22, and he leaves an 18% tip.
What is the total amount Ming pays the cab driver?
Answer:
$25.96
Step-by-step explanation:
Since the tip is 18% of the fare, he pays 118% of the fare.
118% of $22 =
= 1.18 × $22
= $25.96
When comparing the given value to −12, which is a TRUE statement?
8). A wheel which is initially at rest starts to turn with a constant angular acceleration. After 4 seconds it has made 4 complete revolutions. How many revolutions has it made after 8 seconds? b) 16 c) 24
Therefore, the wheel has made 8 complete revolutions after 8 seconds.So, the correct answer is option A) 8.
The given problem is about a wheel that is initially at rest, but then starts to turn with a constant angular acceleration. After four seconds, it has made four complete revolutions. The question asks us to find out how many revolutions it has made after eight seconds.The problem can be solved by using the formula for angular displacement. For a body moving with a constant angular acceleration, the angular displacement, θ can be given as,θ = ω1t + 1/2 α t²Where ω1 is the initial angular velocity and α is the angular acceleration of the body.
Substituting the given values, ω1 = 0 (since the wheel is initially at rest), α is unknown, and t = 4 seconds, we get the equation,[tex]θ = 1/2 α t² = 4 × 2π[/tex]revolutions (since the wheel has made four complete revolutions in four seconds)Solving for α,α = (8π) / (16) = π/2 rad/s²Now, to find out the number of revolutions made after eight seconds, we need to calculate the angular displacement after eight seconds.θ = [tex]ω1t + 1/2 α t²Here, ω1 = 0, α = π/2 rad/s²[/tex], and t = 8 seconds[tex].θ = 0 + 1/2 (π/2) (8)² = 8π[/tex] revolutions
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I need help finding the subsets and proper subsets. Please help it’s due tonight!!
Answer:
Step-by-step explanation:
# elements = 292 - 268 - 1 = 23 elements
G has 2^23 subsets = 8388608
G has 2^23 - 1 proper subsets = 8388607
Oliver practices the piano 448 minutes in 4 weeks. At what rate did she practice, in
minutes per day?
Answer:
16
Step-by-step explanation:
First you figure out how many days are in 4 weeks which is 28. Then you do 448 divided by 28 which equals 16. There's your answer.
How do you tell Linear vs. Nonlinear
Answer:
linear equations produce straight lines when graphed, and their rate of change remains constant
Nonlinear equations do not produce straight lines when graphed.
To determine whether its linear or nonlinear, you can graph it and see if it produces a straight line, or check if it can be written in the form y= Mx+b
Step-by-step explanation:
when using multiple regression techniques, it is common to try out the resulting equation on a second sample to see if it still fits well. this process is known as
The process of trying out the resulting equation on a second sample to see if it still fits well is called “cross-validation”.
Cross-validation is a technique used to evaluate the performance of a statistical model on a new independent dataset, which was not used in training the model. This process helps to assess the generalization capability of the model and helps to determine whether the model is overfitting or underfitting the data. By testing the model on a new independent dataset, we can get a better idea of how well the model is likely to perform on new data in the future. Cross-validation can also help in selecting the best model from a set of competing models.
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NEED ANSWER ASAP NOT WORRIED ABOUT AN EXPLANATION
A quadrilateral has opposite sides with the same slopes and consecutive sides with slopes that are reciprocals. What is the most precise classification of the quadrilateral?
Quadrilateral
Rectangle
Parallelogram
Trapezoid
The most precise classification of the quadrilateral with opposite sides having the same slopes and consecutive sides having slopes that are reciprocals is a Rectangle.
1. Opposite sides with the same slopes imply that these sides are parallel.
2. Consecutive sides with slopes that are reciprocals mean that they are perpendicular.
3. Parallel opposite sides make the quadrilateral a parallelogram.
4. Perpendicular consecutive sides make it a rectangle, as all angles are 90 degrees.
So, the quadrilateral is a Rectangle.
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question: given 2 patterns at 0.4 and 0.6 , estimate probability density analytically using a rectangular window of width 0.3 , using a triangular window of width 0.3 and using 1 nearest-neighbour.
The probability density of the two patterns at 0.4 and 0.6, for one nearest-neighbour is 0.6
Given two patterns at 0.4 and 0.6, the probability density of these patterns can be estimated analytically using a rectangular window of width 0.3, a triangular window of width 0.3, and one nearest-neighbour.
Probability density can be calculated using the following formula: [tex]$p(x)=\frac{n}{aN}$[/tex] where n is the number of samples that fall in the window centered at x, a is the window's width, and N is the total number of samples.
For the rectangular window of width 0.3, the probability density can be calculated as the sum of the two rectangular windows multiplied by 0.3, giving a probability density of 0.6.
For the triangular window of width 0.3, the probability density can be calculated as the sum of the two triangular windows multiplied by 0.3, giving a probability density of 0.45.
Finally, for one nearest-neighbour, the probability density is the maximum of the two patterns, which in this case is 0.6.
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What is the volume of the composite figures?
Total volume of the composite figure using volume of cuboid formula is = 120ft³.
Define volume?A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.
The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.
In the given figure,
Length of cuboid = 6ft.
Breadth of cuboid = 3ft.
Height of cuboid = 5ft.
Length of second cuboid = 4ft.
Height of second cuboid = 5ft.
Breadth of second cuboid = 3ft.
Volume of first cuboid = length × breadth × height.
= 6 × 3 × 5
= 90ft³
Volume of second cuboid = 4 × 3 × 5
= 60ft³
Now the second cuboid is half.
So, volume becomes = 60/2
= 30ft³.
So, total volume of the figure = 90 + 30 = 120ft³.
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A 145 pound person burns 420 calories per hour riding an exercise bicycle at a rate of 15 miles per hour. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem related to the function
Answer: 580
Step-by-step explanation: i learned that just like 1 hour ago in school
at the farmers market there is a large pile of small cauliflowers. the mean weight of these cauliflowers is 400 grams with a standard deviation of 20 grams. assume the weight of theses cauliflowers is normally distributed. which has a greater probability, the mean weight of an individual cauliflower being between 400 and 409 grams or the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams?
The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.
Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:
z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)
μ = 400 grams (mean weight of the population)
σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0
Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:
P(400 < X < 409) = P(0 < Z < 0.45)
Using the standard normal distribution table, the probability is 0.1745.
The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:
(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)
σ = 20 grams (standard deviation)
n = 36 (number of samples)
Now, we need to standardize the sample mean. It will be as follows:
z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)
z = 0
As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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two fair dice are tossed together once
a. draw the sample space for the following outcome
b. find the probability of getting a total of 7 and 8
Therefore, the probability of getting a total of 7 is 6/36, which reduces to 1/6. The probability of getting a total of 8 is 5/36.
What is probability?In mathematics, probability is a measure of the likelihood that an event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. The probability of an event A is denoted by P(A), and it is defined as the ratio of the number of outcomes favorable to A, to the total number of possible outcomes in the sample space.
Here,
a) The sample space for tossing two fair dice can be represented as a table, where each row represents the outcome of one die, and each column represents the outcome of the other die. The sample space for this experiment would consist of all possible combinations of the two dice outcomes. Here's how the sample space table would look like:
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
b) To find the probability of getting a total of 7 or 8, we need to count the number of possible outcomes that result in these totals, and then divide by the total number of possible outcomes in the sample space.
For a total of 7, there are 6 possible outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
=6/36
For a total of 8, there are 5 possible outcomes (2+6, 3+5, 4+4, 5+3, 6+2).
=5/36
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Complete question:
Two fair dice are tossed together once, what is:
a. draw the sample space for the following outcome
b. find the probability of getting a total of 7 and 8
what is fourteen million, six hundred sixty-five thousand, seven hundred eighty-seven in standard form? What is two hundred eighty-six million, nine hundred thousand in standard form?
Answer:
a) 1.4665787 × 10^7
b) 2.869 × 10^8
Step-by-step explanation:
Answer:
14,665,787 that's the answer for that question
Help plis! Need process too
Answer:
Step-by-step explanation:
E
PLEASEEEEE HELPPPPPPP!!!!!!!
A line segment contains endpoints A(-1, 2) and B(2, 5).
Determine the point that partitions line segment AB into a 3: 6 ratio.
A 4,5/3
B 0,3
C 1/3,3
D -2,1
Answer:
We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.
Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:
x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9
y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9
Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:
x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0
y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)
Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.
HELP IS DUE TODAY!!!!!!!!!!!!!!!!!!
Using expressions,
4a. x= 0 is not possible.
4b. x= 1 is not possible.
5a. (9x-5)(9x+5)
5b. (x-3)(2x+1)
6. 1/(3x-7)
7a. x = (-5,∞)
7b. x = (∞,2]
7c. x = (-3,7]
What are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let's examine the writing of expressions.
The other number is x, and a number is 6 greater than half of it.
As a mathematical expression, this proposition is denoted by the expression x/2 + 6.
Here the values of x has to be such that the denominator is not equal to zero.
So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.
a. 81x²-25
= 81x² + 45x-45x-25
=9x(9x+5)-5(9x+5)
= (9x-5)(9x+5)
b. 2x²-5x-3
= 2x² + x - 6x -3
= x(2x+1)-3(2x+1)
=(x-3)(2x+1)
Next, the intervals for x are as follows:
x = (-5,∞)
x = (∞,2]
x = (-3,7]
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suppose is an matrix, all of whose rows are identical. suppose is an matrix, all of whose columns are identical. what can be said about the entries in
we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.
In the row-wise identical matrix, all entries in each row are the same, but the entries in different rows can be different.
In the column-wise identical matrix, all entries in each column are the same, but the entries in different columns can be different.
Thus, we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.
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